
********************************************************************************
**
**  E 1 2 _ C o m b i n a t i o n s _ 2 _ B . t x t
**
********************************************************************************
**
**  FUNCTIONAL DESCRIPTION
**
**  This text file contains a concise table of feasible combinations of the
**  form 1/X = 1/x1 + 1/x2, where x1 and x2 are two values taken from the E12
**  series of preferred values and X is the resulting value of this combina-
**  tion. The different E series of preferred values are specified in IEC
**  Standard 60063.
**
**  The E12 series consists of the following 12 base values:
**
**  100  120  150  180  220  270  330  390  470  560  680  820
**
**  The above type of combinations applies to parallel connections of two
**  resistors, parallel connections of two inductors, or series connections of
**  two capacitors, respectively. The latter two cases, however, are of minor
**  practical importance. Single values are seamlessly included, in which case
**  one of the x values is infinite.
**
**  In order to limit the potentially infinite number of possible combinations
**  to a reasonable amount, combinations where the ratio between the largest
**  finite value and the smallest non-zero value would exceed an upper limit
**  of 100 are excluded. Such an upper limit corresponds to nominal component
**  tolerances in the order of 1% for the dominant values of a combination,
**  which should be sufficient for most cases of interest. Also, equivalent
**  permutations are eliminated by ensuring that x1 <= x2.
**
**  The table of feasible combinations below is sorted in ascending order of
**  resulting values X, and these values are normalised such that they gener-
**  ally fall into the base decade from 100 to 1000, thus 100 <= X < 1000. Of
**  course, all table entries can be arbitrarily scaled up or down by factors
**  of 10, 100, 1000, and so forth.
**
**  This is best illustrated with resistors:
**
**              ____ r1
**        +----|____|----+
**  o-----+     ____ r2  +-----o
**        +----|____|----+
**
**  r1..r2 = resistance values of the used resistors
**  R = total resistance of the resistor combination
**  M = maximum allowed ratio of resistance values
**
**  M = 100
**  1/R = 1/r1 + 1/r2
**  100 <= R < 1000
**  r1 <= r2
**  r2 may be infinite (one resistor)
**  1 <= r2/r1 <= M ;   if r2 < inf
**
**  All in all, the resulting table of feasible combinations contains a total
**  of 312 entries. As some values can be realised in different ways, however,
**  there are only 310 distinct values. The maximum relative difference be-
**  tween adjacent values is 3.1977 percent.
**
**  The normalised relative uncertainty (NRU) value, which is also given for
**  each combination, is calculated via the common error propagation formula
**  for independent variables and gives an estimate for the mean relative
**  uncertainty of the resulting value X of this combination in relation to
**  the mean relative uncertainties of its x values. This estimate is valid
**  under the simplifying assumption that the x values are statistically inde-
**  pendent and normally distributed about their nominal values and that they
**  have identical relative uncertainties, in which case 0.707 <= NRU <= 1.
**
**  This means that the relative dispersion of the resulting value X of a
**  combination is somewhat reduced compared to the relative dispersions of
**  its individual x values. The worst-case behaviour is not improved, though.
**  Note, however, that the above independence assumption may already be vio-
**  lated when a combination is made up of components from the same production
**  batch, just to name one potential caveat.
**
**  One last note on the file format: This is a Unix plain text file that uses
**  single line-feed (LF) characters as line terminators and assumes a fixed
**  tab spacing of eight characters. Thus, a monospaced font and proper tab
**  settings are recommended for best readability; and on Windows, it may be
**  necessary, too, to replace LF with CR LF.
**
********************************************************************************
**
**  VERSION HISTORY
**
**  Author:     Gert Willmann, Stuttgart, Germany
**
**  Version:    1.0, 30-Jul-2017 (15724 bytes)
**
**  Copyright:  (C) 2017 Gert Willmann
**
**  This file is free software; it can be redistributed and/or modified under
**  the terms of the GNU Lesser General Public License (LGPL) as published by
**  the Free Software Foundation, either Version 3 of the License or (at your
**  option) any later version.
**
**  This file is distributed in the hope that it will be useful, but without
**  any warranty; without even the implied warranty of merchantability or fit-
**  ness for a particular purpose. See the GNU Lesser General Public License
**  for more details.
**
**  A copy of the GNU Lesser General Public License should have come along
**  with this file. If not, see <http://www.gnu.org/licenses/>.
**
********************************************************************************



Table of Combinations:
======================

--------------------------------------------------------
Line	X		x1	x2	NRU	Series
--------------------------------------------------------
1	100		100	-	1	E3
2	102		120	680	0.863	E12
3	103.125		150	330	0.755	E6
4	104.68085106	120	820	0.882	E12
5	107.14285714	120	1k	0.899	E12
6	108		180	270	0.721	E12
7	108.33333333	150	390	0.774	E12
8	109.09090909	120	1.2k	0.914	E12
9	110		220	220	0.707	E3
10	111.11111111	120	1.5k	0.929	E12
11	112.5		120	1.8k	0.94	E12
12	113.70967742	150	470	0.796	E6
13	113.79310345	120	2.2k	0.95	E12
14	114.89361702	120	2.7k	0.958	E12
15	115.78947368	120	3.3k	0.966	E12
16	116.41791045	120	3.9k	0.971	E12
17	116.47058824	180	330	0.737	E12
18	117.01244813	120	4.7k	0.975	E12
19	117.48251748	120	5.6k	0.979	E12
20	117.91907514	120	6.8k	0.983	E12
21	118.26923077	120	8.2k	0.986	E12
22	118.30985915	150	560	0.817	E12
23	118.5770751	120	10k	0.988	E12
24	118.81188119	120	12k	0.99	E12
25	120		120	-	1	E12
26	121.2244898	220	270	0.711	E12
27	122.89156627	150	680	0.839	E6
28	123.15789474	180	390	0.754	E12
29	126.80412371	150	820	0.859	E12
30	130.15384615	180	470	0.774	E12
31	130.43478261	150	1k	0.879	E6
32	132		220	330	0.721	E6
33	133.33333333	150	1.2k	0.896	E12
34	135		270	270	0.707	E12
35	136.21621622	180	560	0.795	E12
36	136.36363636	150	1.5k	0.914	E6
37	138.46153846	150	1.8k	0.926	E12
38	140.42553191	150	2.2k	0.938	E6
39	140.6557377	220	390	0.734	E12
40	142.10526316	150	2.7k	0.949	E12
41	142.3255814	180	680	0.818	E12
42	143.47826087	150	3.3k	0.958	E6
43	144.44444444	150	3.9k	0.964	E12
44	145.36082474	150	4.7k	0.97	E6
45	146.08695652	150	5.6k	0.974	E12
46	146.76258993	150	6.8k	0.979	E6
47	147.30538922	150	8.2k	0.982	E12
48	147.6		180	820	0.84	E12
49	147.78325123	150	10k	0.985	E6
50	148.14814815	150	12k	0.988	E12
51	148.5		270	330	0.711	E12
52	148.51485149	150	15k	0.99	E6
53	149.85507246	220	470	0.752	E3
54	150		150	-	1	E6
55	152.54237288	180	1k	0.861	E12
56	156.52173913	180	1.2k	0.879	E12
57	157.94871795	220	560	0.771	E12
58	159.54545455	270	390	0.719	E12
59	160.71428571	180	1.5k	0.899	E12
60	163.63636364	180	1.8k	0.914	E12
61	165		330	330	0.707	E6
62	166.22222222	220	680	0.794	E6
63	166.38655462	180	2.2k	0.927	E12
64	168.75		180	2.7k	0.94	E12
65	170.68965517	180	3.3k	0.95	E12
66	171.48648649	270	470	0.732	E12
67	172.05882353	180	3.9k	0.957	E12
68	173.36065574	180	4.7k	0.964	E12
69	173.46153846	220	820	0.816	E12
70	174.39446367	180	5.6k	0.969	E12
71	175.35816619	180	6.8k	0.975	E12
72	176.13365155	180	8.2k	0.979	E12
73	176.8172888	180	10k	0.982	E12
74	177.33990148	180	12k	0.985	E12
75	177.86561265	180	15k	0.988	E12
76	178.21782178	180	18k	0.99	E12
77	178.75		330	390	0.71	E12
78	180		180	-	1	E12
79	180.32786885	220	1k	0.839	E3
80	182.1686747	270	560	0.749	E12
81	185.91549296	220	1.2k	0.859	E12
82	191.86046512	220	1.5k	0.881	E6
83	193.26315789	270	680	0.77	E12
84	193.875		330	470	0.718	E6
85	195		390	390	0.707	E12
86	196.03960396	220	1.8k	0.898	E12
87	200		220	2.2k	0.914	E3
88	203.11926606	270	820	0.792	E12
89	203.42465753	220	2.7k	0.928	E12
90	206.25		220	3.3k	0.94	E6
91	207.64044944	330	560	0.73	E12
92	208.25242718	220	3.9k	0.948	E12
93	210.16260163	220	4.7k	0.956	E3
94	211.6838488	220	5.6k	0.963	E12
95	212.5984252	270	1k	0.816	E12
96	213.10541311	220	6.8k	0.969	E6
97	213.13953488	390	470	0.71	E12
98	214.25178147	220	8.2k	0.974	E12
99	215.26418787	220	10k	0.979	E3
100	216.03927987	220	12k	0.982	E12
101	216.81997372	220	15k	0.986	E6
102	217.34357849	220	18k	0.988	E12
103	217.82178218	220	22k	0.99	E3
104	220		220	-	1	E3
105	220.40816327	270	1.2k	0.837	E12
106	222.17821782	330	680	0.748	E6
107	228.81355932	270	1.5k	0.861	E12
108	229.89473684	390	560	0.718	E12
109	234.7826087	270	1.8k	0.879	E12
110	235		470	470	0.707	E3
111	235.30434783	330	820	0.769	E12
112	240.48582996	270	2.2k	0.897	E12
113	245.45454545	270	2.7k	0.914	E12
114	247.85046729	390	680	0.733	E12
115	248.12030075	330	1k	0.792	E6
116	249.57983193	270	3.3k	0.927	E12
117	252.51798561	270	3.9k	0.937	E12
118	255.33199195	270	4.7k	0.947	E12
119	255.53398058	470	560	0.71	E12
120	257.58091993	270	5.6k	0.955	E12
121	258.82352941	330	1.2k	0.813	E12
122	259.68882603	270	6.8k	0.963	E12
123	261.3931523	270	8.2k	0.969	E12
124	262.90165531	270	10k	0.974	E12
125	264.05867971	270	12k	0.978	E12
126	264.29752066	390	820	0.75	E12
127	265.2259332	270	15k	0.982	E12
128	266.00985222	270	18k	0.985	E12
129	266.72653794	270	22k	0.988	E12
130	267.32673267	270	27k	0.99	E12
131	270		270	-	1	E12
132	270.49180328	330	1.5k	0.839	E6
133	277.91304348	470	680	0.719	E6
134	278.87323944	330	1.8k	0.859	E12
135	280		560	560	0.707	E12
136	280.57553957	390	1k	0.772	E12
137	286.95652174	330	2.2k	0.879	E6
138	294.05940594	330	2.7k	0.898	E12
139	294.33962264	390	1.2k	0.794	E12
140	298.75968992	470	820	0.733	E12
141	300		330	3.3k	0.914	E6
142	304.25531915	330	3.9k	0.925	E12
143	307.09677419	560	680	0.71	E12
144	308.3499006	330	4.7k	0.937	E6
145	309.52380952	390	1.5k	0.82	E12
146	311.63575042	330	5.6k	0.946	E12
147	314.72650771	330	6.8k	0.955	E6
148	317.23329426	330	8.2k	0.962	E12
149	319.45788964	330	10k	0.969	E6
150	319.72789116	470	1k	0.752	E3
151	320.54794521	390	1.8k	0.841	E12
152	321.16788321	330	12k	0.974	E12
153	322.8962818	330	15k	0.979	E6
154	324.0589198	330	18k	0.982	E12
155	325.12315271	330	22k	0.985	E6
156	326.01536773	330	27k	0.988	E12
157	326.73267327	330	33k	0.99	E6
158	330		330	-	1	E6
159	331.27413127	390	2.2k	0.863	E12
160	332.75362319	560	820	0.72	E12
161	337.7245509	470	1.2k	0.772	E12
162	340		680	680	0.707	E6
163	340.77669903	390	2.7k	0.883	E12
164	348.7804878	390	3.3k	0.901	E12
165	354.54545455	390	3.9k	0.914	E12
166	357.8680203	470	1.5k	0.798	E6
167	358.97435897	560	1k	0.735	E12
168	360.11787819	390	4.7k	0.927	E12
169	364.60767947	390	5.6k	0.937	E12
170	368.84561892	390	6.8k	0.947	E12
171	371.73333333	680	820	0.71	E12
172	372.29336438	390	8.2k	0.956	E12
173	372.68722467	470	1.8k	0.82	E12
174	375.36092397	390	10k	0.963	E12
175	377.72397094	390	12k	0.969	E12
176	380.11695906	390	15k	0.975	E12
177	381.72920065	390	18k	0.979	E12
178	381.81818182	560	1.2k	0.752	E12
179	383.20678874	390	22k	0.983	E12
180	384.44687842	390	27k	0.986	E12
181	385.44474394	390	33k	0.988	E12
182	386.13861386	390	39k	0.99	E12
183	387.2659176	470	2.2k	0.843	E3
184	390		390	-	1	E12
185	400.31545741	470	2.7k	0.865	E12
186	404.76190476	680	1k	0.72	E6
187	407.76699029	560	1.5k	0.777	E12
188	410		820	820	0.707	E12
189	411.40583554	470	3.3k	0.884	E6
190	419.45080092	470	3.9k	0.899	E12
191	427.11864407	560	1.8k	0.799	E12
192	427.27272727	470	4.7k	0.914	E3
193	433.60790774	470	5.6k	0.926	E12
194	434.04255319	680	1.2k	0.734	E12
195	439.61485557	470	6.8k	0.938	E6
196	444.52133795	470	8.2k	0.947	E12
197	446.37681159	560	2.2k	0.823	E12
198	448.90162369	470	10k	0.956	E3
199	450.54945055	820	1k	0.711	E12
200	452.28548516	470	12k	0.963	E12
201	455.72074984	470	15k	0.97	E6
202	458.04006497	470	18k	0.975	E12
203	460.16911437	470	22k	0.979	E3
204	461.95850018	470	27k	0.983	E12
205	463.40005976	470	33k	0.986	E6
206	463.80368098	560	2.7k	0.846	E12
207	464.40334431	470	39k	0.988	E12
208	465.34653465	470	47k	0.99	E3
209	467.88990826	680	1.5k	0.755	E6
210	470		470	-	1	E3
211	478.75647668	560	3.3k	0.867	E12
212	487.12871287	820	1.2k	0.72	E12
213	489.68609865	560	3.9k	0.883	E12
214	493.5483871	680	1.8k	0.776	E12
215	500		1k	1k	0.707	E3
216	500.38022814	560	4.7k	0.9	E12
217	509.09090909	560	5.6k	0.914	E12
218	517.39130435	560	6.8k	0.927	E12
219	519.44444444	680	2.2k	0.8	E6
220	524.20091324	560	8.2k	0.938	E12
221	530.17241379	820	1.5k	0.737	E12
222	530.3030303	560	10k	0.948	E12
223	535.03184713	560	12k	0.956	E12
224	539.84575835	560	15k	0.965	E12
225	543.10344828	560	18k	0.97	E12
226	543.19526627	680	2.7k	0.824	E12
227	545.45454545	1k	1.2k	0.71	E12
228	546.09929078	560	22k	0.975	E12
229	548.62119013	560	27k	0.98	E12
230	550.65554231	560	33k	0.983	E12
231	552.07280081	560	39k	0.986	E12
232	553.40622372	560	47k	0.988	E12
233	554.45544554	560	56k	0.99	E12
234	560		560	-	1	E12
235	563.35877863	820	1.8k	0.755	E12
236	563.81909548	680	3.3k	0.847	E6
237	579.03930131	680	3.9k	0.864	E12
238	594.05204461	680	4.7k	0.883	E6
239	597.35099338	820	2.2k	0.777	E12
240	600		1k	1.5k	0.721	E6
241	600		1.2k	1.2k	0.707	E12
242	606.36942675	680	5.6k	0.898	E12
243	618.18181818	680	6.8k	0.914	E6
244	627.92792793	680	8.2k	0.927	E12
245	628.97727273	820	2.7k	0.802	E12
246	636.70411985	680	10k	0.938	E6
247	642.85714286	1k	1.8k	0.735	E12
248	643.53312303	680	12k	0.948	E12
249	650.51020408	680	15k	0.958	E6
250	655.24625268	680	18k	0.964	E12
251	656.7961165	820	3.3k	0.825	E12
252	659.61199295	680	22k	0.97	E6
253	663.29479769	680	27k	0.976	E12
254	666.27078385	680	33k	0.98	E6
255	666.66666667	1.2k	1.5k	0.711	E12
256	668.34677419	680	39k	0.983	E12
257	670.30201342	680	47k	0.986	E6
258	671.84191955	680	56k	0.988	E12
259	673.26732673	680	68k	0.99	E6
260	677.54237288	820	3.9k	0.844	E12
261	680		680	-	1	E6
262	687.5		1k	2.2k	0.755	E3
263	698.1884058	820	4.7k	0.864	E12
264	715.26479751	820	5.6k	0.882	E12
265	720		1.2k	1.8k	0.721	E12
266	729.72972973	1k	2.7k	0.778	E12
267	731.75853018	820	6.8k	0.899	E12
268	745.45454545	820	8.2k	0.914	E12
269	750		1.5k	1.5k	0.707	E6
270	757.85582255	820	10k	0.927	E12
271	767.44186047	1k	3.3k	0.802	E6
272	767.55070203	820	12k	0.938	E12
273	776.47058824	1.2k	2.2k	0.737	E12
274	777.49683944	820	15k	0.95	E12
275	784.27205101	820	18k	0.957	E12
276	790.53461876	820	22k	0.965	E12
277	795.83033789	820	27k	0.971	E12
278	795.91836735	1k	3.9k	0.822	E12
279	800.11827321	820	33k	0.976	E12
280	803.11401306	820	39k	0.98	E12
281	805.93893768	820	47k	0.983	E12
282	808.16613868	820	56k	0.986	E12
283	810.22958442	820	68k	0.988	E12
284	811.88118812	820	82k	0.99	E12
285	818.18181818	1.5k	1.8k	0.71	E12
286	820		820	-	1	E12
287	824.56140351	1k	4.7k	0.843	E3
288	830.76923077	1.2k	2.7k	0.758	E12
289	848.48484848	1k	5.6k	0.862	E12
290	871.79487179	1k	6.8k	0.881	E6
291	880		1.2k	3.3k	0.78	E12
292	891.30434783	1k	8.2k	0.898	E12
293	891.89189189	1.5k	2.2k	0.72	E6
294	900		1.8k	1.8k	0.707	E12
295	909.09090909	1k	10k	0.914	E3
296	917.64705882	1.2k	3.9k	0.8	E12
297	923.07692308	1k	12k	0.926	E12
298	937.5		1k	15k	0.94	E6
299	947.36842105	1k	18k	0.949	E12
300	955.93220339	1.2k	4.7k	0.822	E12
301	956.52173913	1k	22k	0.958	E3
302	964.28571429	1k	27k	0.965	E12
303	964.28571429	1.5k	2.7k	0.735	E12
304	970.58823529	1k	33k	0.971	E6
305	975		1k	39k	0.975	E12
306	979.16666667	1k	47k	0.979	E3
307	982.45614035	1k	56k	0.983	E12
308	985.50724638	1k	68k	0.986	E6
309	987.95180723	1k	82k	0.988	E12
310	988.23529412	1.2k	5.6k	0.842	E12
311	990		1.8k	2.2k	0.711	E12
312	990.0990099	1k	100k	0.99	E3
--------------------------------------------------------
